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Home/Chain Registry/Block #666,933

Block #666,933

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2014, 8:56:42 AM Β· Difficulty 10.9618 Β· 6,160,050 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
f7dee0ddc7aae3a1ae01761d3db63b6448e31d876b87405ff444c86f5fbd06f7
View on Chainz β†—

Height

#666,933

Difficulty

10.961802

Transactions

1

Size

207 B

Version

2

Bits

0af638ae

Nonce

1,300,131,738

Timestamp

8/7/2014, 8:56:42 AM

Confirmations

6,160,050

Merkle Root

69b470d5315433142b602f7ee8e3e04735865c85759dc1860c82e851abc008da
Transactions (1)
Coinbase69b470d5315433…82e851abc008da
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.515 Γ— 10⁹⁢(97-digit number)
75155925595919479453…68456953699037766400
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
7.515 Γ— 10⁹⁢(97-digit number)
75155925595919479453…68456953699037766401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.503 Γ— 10⁹⁷(98-digit number)
15031185119183895890…36913907398075532801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.006 Γ— 10⁹⁷(98-digit number)
30062370238367791781…73827814796151065601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.012 Γ— 10⁹⁷(98-digit number)
60124740476735583562…47655629592302131201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.202 Γ— 10⁹⁸(99-digit number)
12024948095347116712…95311259184604262401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.404 Γ— 10⁹⁸(99-digit number)
24049896190694233425…90622518369208524801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.809 Γ— 10⁹⁸(99-digit number)
48099792381388466850…81245036738417049601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.619 Γ— 10⁹⁸(99-digit number)
96199584762776933700…62490073476834099201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.923 Γ— 10⁹⁹(100-digit number)
19239916952555386740…24980146953668198401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.847 Γ— 10⁹⁹(100-digit number)
38479833905110773480…49960293907336396801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 666933

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock f7dee0ddc7aae3a1ae01761d3db63b6448e31d876b87405ff444c86f5fbd06f7

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #666,933 on Chainz β†—
Circulating Supply:57,860,038 XPMΒ·at block #6,826,982 Β· updates every 60s
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